Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D15×C361⋊C3 |
| unambiguous semidirect product | C3⋊(D5×C361⋊C3) |
| unambiguous semidirect product | C5⋊(D3×C361⋊C3) |
| unambiguous semidirect product | (D15×C361)⋊C3 |
| Fitting, derived | C3×C5×C361 ⋊ C2×C3 |
| Hall | C3×C5×C361⋊C3 ⋊ C2 |
| Hall | C3×C361⋊C3 ⋊ D5 |
| Hall | C5×C361 ⋊ C3×D3 |
| Sylow | C361 ⋊ C3×D15 |
| Sylow | C5 ⋊ D3×C361⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C361 | C2×C3 |
| Frattini | C19 | D15×C19⋊C3 |
| socle | C3×C5×C19 | C2×C19⋊C3 |
| LCS | G ▷ C3×C5×C361 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5415 |
1107 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 23);